where the double exclamation point mean we multiply all the odd numbers less or equal to the number (e.g \(7!! = 1\cdot 3\cdot 5\cdot 7 = 105\) ). The expression for \(x_{01}\)  is taken from [1]} and [2]}. Notice that the notation for the series above in [1]} is different: they take \(\tau = \frac{\varphi }{30}\) . The expressions for the other periods are taken from [4]}. To find the period matrix in terms of \(x_{ij}\) , we need to change from \(\tilde{\eta }\)  to the basis \(\alpha \)  from the moduli space. We consider, therefore, the matrices
\(S=\left(\begin{array}{ccccc}1 & 0 & 0 & 0 & 0\\0 & 1 & 0 & 0 & 0 \\0 &-5^{5} & -5^{4}(z-1) & 0 & 0 \\0 & -\frac{5}{z-1} & 0 & 1 & 0 \\0 & 0 & 0 & 0 & 5^{4}(z-1)\end{array}\right)\) 
